Cos 5pi 3

What is the function value for P (t) = 20 cos 5pi / 3 t +100? 3

The answer on my answer sheet is 6/5, but I need to know how to do it.

Thanks in advance for the help.

First, the specific expression is not clear, it could be: 20 * cos (5pi * t / 3) + 100 or 20 * cos (5pi * t / 3 + 100). It is not clear if t is in denominator and 100 is in cosine. The answer you have given solves the riddle, it is difficult and it does not matter where 100 is (see below).

Let's do this one by one. Let's go back to cos (t) and move on to the action assigned to it.

First, the value of the function is the distance between the input values that causes the pattern graph to repeat. So, consider the simple function cos (t), whose cosine is normal 2pi. That is, the graph of cos (t) looks exactly like the graph of cos (t + 2pi). Let's look at the graph of cos (t) with any value, then look at the total 2pi, graph it, and see that the graphs look exactly the same.

So I'm in cos (t) with 2pi. When I multiply t by a value, I divide by the same value to get a new one. So cos (t) is 2pi and cos (2t) is 2pi / 2 = pi.

So if I have cos (5pi * t / 3), I have multiplied the ■■■■ content of cosine by 5pi / 3, so now I have to divide the 2pi ■■■■ by 5pi / 3. With mutual value, I now have to do 2pi * 3 / (5pi) which is equal to 6pi / (5pi) which is equal to 6/5.

But we haven't worked yet, look at the cosine coefficient of 20. What changes if the cosine factor is multiplied by 20? The answer is no, no. Multiplying the cosine by the number spreads the function vertically, i.e. the length of the value on the H. X axis on the y axis does not change. You will notice that cos (t) and 5 * cos (t) cross the x-axis at exactly the same place and this is exactly where they repeat. If you are not sure, I invite you to do some calculator work.

Finally, let's try adding 100 so that you get the function in your problem. I don't know if 100 cosine is in or out, so take a closer look. What if you add 100 [for example H. cos (5pi * t / 3) + 100]? And the answer is no. Taking a graph and moving it up or down (in this case) does not change the normally repeated graph, it only determines where the graph is. Similarly, adding 100 to the cosine does not change anything because it only shifts the function left or right on the X axis, because adding a constant value to a variable changes it to only one constant value. t Increase the value of the variable.

So you go with 6/5.